It is confusing for everyone outside the UK.

When learning English in France, you are taught about these British naming quite early and it is always a surprise for the children.

It is not even that there are specific needles for theses schools, rather the fact that a public school is not for the public.

It's deliberately so and used as an in group marker.

There are also complex unwritten rules governing dress, speech and general manors that serve the same purpose.

There are some job interviews you better not turn up to wearing the wrong colour shoes or shirt.

Personally, I blame the Normans.

> It's deliberately so [confusing]

This is not true. Public schools pre-date modern state schools and what made them "public", by the original definition, was that they were open to any child - provided that their parents could afford the fees.

Other private schools at the time were open only to the children of parents who met certain criteria, and hence were not "public".

I would say that it is confusing to anyone else apart the people from the UK, "public" is usually understood as "public" (as opposed to "private").

"Public [School in England]" = "Publicly accessible, (in general) open to people [ - anyone can enrol]"

In other cases, "Public [entity]" = "paid by the people".